Problem: Simplify; express your answer in exponential form. Assume $t\neq 0, z\neq 0$. $\dfrac{{(t^{4})^{4}}}{{(t^{-1}z^{-4})^{-5}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{4}}$ to the exponent ${4}$ . Now ${4 \times 4 = 16}$ , so ${(t^{4})^{4} = t^{16}}$ In the denominator, we can use the distributive property of exponents. ${(t^{-1}z^{-4})^{-5} = (t^{-1})^{-5}(z^{-4})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{4})^{4}}}{{(t^{-1}z^{-4})^{-5}}} = \dfrac{{t^{16}}}{{t^{5}z^{20}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{16}}}{{t^{5}z^{20}}} = \dfrac{{t^{16}}}{{t^{5}}} \cdot \dfrac{{1}}{{z^{20}}} = t^{{16} - {5}} \cdot z^{- {20}} = t^{11}z^{-20}$.